You certainly *could* do it. It's just a question of whether you're willing to schedule your brew day around it. Under ideal conditions, an 1800 W element would heat 15 gal to strike temperatures in about two hours, take an hour to get from lauter to a boil, and boil off ~0.7 gal/hr once at a boil.
I use a 120 V element for my hot liquor, and just set it to turn on a couple hours before I want to brew using an outlet timer. The timer controls a relay since I doubt the little plastic box could handle 15 A.